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We discuss the recent developments in the theory of diffusive shock acceleration (DSA) by using both first-principle kinetic plasma simulations and analytical theory based on the solution of the convection/diffusion equation. In particular,…
In this paper we present a novel approach to FEL simulations based on the decomposition of the electromagnetic field in a finite number of radiation modes. The evolution of each mode amplitude is simply determined by energy conservation.…
Strong convergence rates for (temporal, spatial, and noise) numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood in the scientific literature. Weak…
We develop a general method allowing one to construct the consistent theory of light pulse propagation through an atomic medium in arbitrary nonlinear regime with respect to the field strength, taking into account the light polarization,…
Fundamental to many applications of laser pulses in science and technology is an extended interaction length with matter that significantly exceeds the distance over which the pulse would normally diffract and transversely spread. At low…
Partial Differential Equations (PDEs) models for wave propagation in inhomogeneous media are relevant for many applications. We will discuss numerical methods tailored for tackling problems governed by these variable-coefficient PDEs.…
In this research, numerical analysis of nonlinear pulse propagation is carried out. This is done mainly by solving the nonlinear Schrodinger equation using the split step algorithm. In a nonlinear media, dispersive effects exist…
We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation…
We have developed a computational method to describe the nonlinear light propagation of an intense and ultrashort pulse at oblique incidence on a flat surface. In the method, coupled equations of macroscopic light propagation and…
The propagation of the wave function of a particle is characterised by a group and a phase velocity. The group velocity is associated with the particle's classical velocity, which is always smaller than the speed of light, and the phase…
The problem of radio wave reflection from an optically thick plane monotonous layer of magnetized plasma is considered at present work. The plasma electron density irregularities are described by spatial spectrum of an arbitrary form. The…
We present angle- and polarization-resolved measurements of the optical transmission of a subwavelength hole array. These results give a (far-field) visualization of the corresponding (near-field) propagation of the excited surface plasmons…
The GN model of non-linear fiber propagation has been shown to overestimate the variance of non-linearity due to the signal Gaussianity approximation, leading to maximum reach predictions for realistic optical systems which may be…
We consider short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. In the frequency "band gaps" (where linear electromagnetic waves are evanescent) with linear…
The effect of the thickness of the dielectric boundary layer that connects a material of refractive index $n_1$ to another of index $n_2$ is considered for the propagation of an electromagnetic pulse. For very thin boundary layer the…
A time-resolved analysis of the amplitude and phase of THz pulses propagating through three-dimensional photonic crystals is presented. Single-cycle pulses of THz radiation allow measurements over a wide frequency range, spanning more than…
Kinetic plasma studies often require computing integrals of the velocity distribution over a complex-valued pole. The standard method is to solve the integral in the complex plane using the Plemelj theorem, resulting in the standard plasma…
For one dimensional homogeneous bistable diffusion equations, Fife-McLeod ([Arch. Ration. Mech. Anal., 65 (1977), 335-361]) gave a well-known theorem which says that spreading solutions starting from compactly supported initial data can be…
In this manuscript we investigate the capabilities of the Discrete Dipole Approximation (DDA) to simulate scattering from particles that are much larger than the wavelength of the incident light, and describe an optimized publicly available…
Fractional calculus, in allowing integrals and derivatives of any positive order (the term "fractional" kept only for historical reasons), can be considered a branch of mathematical physics which mainly deals with integro-differential…